What is the area of yhe region in the first quadrant defined by y=x^2 and y=4

Q: Find the area of the region in the first quadrant bounded by the line y=2​x x=4​ y=2/x and the​…

A: The given region is bounded in first quadrant by following curve: y=2xx=4y=2x and the x-axis.…

Q: Find the area of the region between the curve y 4 In x and the horizontal axis for

A: We have to find the area of the region between the curve  y=4 ln x and the horizontal axis for…

Q: Find the area bounded by the parabola y^2=4x and the line 2x-4. (with graph)

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Q: Find the area bounded by the curve y=4x-x² and the lines x=-2 and y=4.

A: See below

Q: Find the area bounded by the parabola y2 − 3x + 3 = 0 and the line x = 4. With illustrations please

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Q: Find the area bounded by tHe curves y=8x-x and y= 3x

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Q: The area between the two curves in the picture is

A: GIven functions are, y1=4y2=x2The given graphs are symmetric about y axis.The points of intersection…

Q: What is the area of the region enclosed by the curve y=x(x-1) (x-2) and the x-axis?

A: Given:            Curve: y=xx-1x-2             Area =∫01xx-1x-2 dx+-1∫12xx-1x-2 dx…

Q: The method of washer is used to find the area between curves. True False

A: follow next step

Q: What is the area of the region between the lines y = 7x and y = 3x from x = 1 to x = 4?

A: 1.

Q: Find the area bounded by the indicated curves. y = x4 - 18x? + 81, y = 81 - x

A:

Q: Calculate the area of the segment cut from the curve y = x(3 – x) by the line y = x.

A: here we have to find the area of the region bounded by the curve and line.

Q: What is the area of the region bounded by the y axis with lines?

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Q: What is the area of the region between the graps y = x – 1 and line y = -x – 1

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Q: Find the area bounded by the curve y=x^2 − 4, the lines y = 0 and x = 4

A: The graph is shown below:

Q: Find the area of the region bounded by the curve y = 9 - x2 and the x-axis.

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Q: Please estimate the area under the curve c(x)=1−x3 for 0≤x≤1 using 4 rectangles with width 1/4.

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Q: What is the area of the region enclosed by the curve y=x^2 and the lines y=x+6, x=0 and x=5?

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Q: By double integration, Find the area between the line y=6-2x, the x-axis and y-axis.

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Q: Find the area bounded by the curve y = 3x – x3 and the line y = 2

A: Given: y= 3x-x3; y=2 If f(x)> g(x) in the interval x=a to x=b, then the area between two curves…

Q: Sketch the signed arearepresented by the intergal.Indicate the regionsof positive and negative area.

A: Therefore, the value of the integral is 0.23286.

Q: Find the area of the region bounded by y = 5x², y=0, x= 4, x = 6. Give your answer to the nearest…

A: Sol:- The area between curves is the area between a curve fx and a curve gx on an interval a, b…

Q: Find the area of teh region bounded by y=5x/x2+2, x=1, x=5, y=0. Sketch the graph

A: We graph the region using a graphing calculator.

Q: Determine the area bounded by the curve y = 2x - x^2 + 5 and the line joining the points (3,2) and…

A: Please see the explanation below

Q: Find the total area of the shaded region. 10- y = 8 6- 4- y=8 cosx 2- 1/2 元 Зл/2

A: Given curve y=8cos2x  liney=8

Q: Find the area between the curves. x = -5, x=2, y = 3x, y = x² - 4

A:

Q: Two curves having an equation of 2y² and y = 2x² x = intersect each other. Compute the area between…

A: A detailed solution is given below.

Q: Find the area of the region bounded by y = 4x + 9, y = -6x + 9 and x = 14. Leave your answer correct…

A: Area of region bounded by given curves are evaluated.

Q: estimate the area under the curve y=x^1/2, from x=1 to x=3 using right end point estimate

A: SolutionGiventhe curve y=x,from x=1tox=3 we need to estimate the area  under the curve y=x1/2,from…

Q: Find the area between the curve y = 9 − (x/2)^2 and the line y = 6 − x.

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Q: Find the area on the first quadrant bounded by the curve y = 2Vx and the lines y = 1,x = 4 and the…

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Q: Find the area of the region between the curves 4x + y = 12 and x = y. Area between curves

A: Solution

Q: Find the area of the region bounded by the curve  y = 2x2 - x  and the line  y = x + 4  .

A: To find the area of the curve.

Q: $ find the area of region in the first quadrant bounded on the left by the y-axis, below by curve x…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: The area of the region bounded by x = /9-y', the y-axis and the line x-y in the first quadrant is:

A:

Q: Calculate the area between the curves x = 1– y² by the line x = y² – 1.

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Q: What is the area (in square units) of the region bounded by the graphs of y=x+2, and the x axis from…

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Q: Find the area between the curves y = 4x° and y= 3x + 1.

A: Given the curves y=4x2 and curve y=3x+1. We need to find the area between two curves.

Q: Find the area of the region which is bounded by y = sin x - 2, y = 4x, y-axis and x = 2. Leave your…

A:

Q: Find the area of the region between the curves 4x + y = 12 and x = y. Area between curves =

A: R

Q: Find the area of the region which is bounded by y = sin x - 4, y = 4x, y-axis and x = 4. Leave your…

A: Please refer the attached image for complete solution. THANK YOU.

Q: Find the area of the region bounded by the curve y= 1--x² and the x-axis.

A: Given equation of the curve: y=1-19x2 To find: Area of the region bounded by the curve and x-axis.

Q: Find the area of the region bounded by y = 7x + 7, y = -9x + 4 and x = 15. Leave your answer correct…

A: The solution of the problem is given in the next steps.

Q: Find the area bounded by the curves, 2x² + 4x + y =0 and y = 2x.

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Q: Estimate the area of the region under the curve        y = -x3 + 5 and above the x-axis for…

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Q: Find the area of the region bounded by the line y = 2x – 5 and the parabola y = x² – 4x. - -

A: Graph of enclosed region -

Q: find the area of the region bounded by the curve y=x2 - 4x+3  , x axis and the lines x=2 and x=4

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Q: Find the area of the region bounded by the curve y=1--x2 and the x-axis. 9

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Q: Find the area of the region in the first quadrant bounded by the line y = 8x, the line x = 1, the…

A: Intersection Points are:  The line x=1 will intersect the x-axis at (1,0) because y is 0 at…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.